This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalises the critical groups of complex finite group representations studied in [1, 11]. A formula is given for the cardinality of the critical group generally, and the critical group for the regular representation is described completely. A key role in the formulas is played by the greatest common divisor of the dimensions of the indecomposable projective representations.
|Original language||English (US)|
|Number of pages||31|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|State||Published - 2020|
Bibliographical noteFunding Information:
† Supported by NSF grants DMS-1148634, 1601961.